Dave Gudeman comments<\/a>:<\/span><\/p>\n I was surprised to see you distinguishing between bivalence and the LEM. As far as I can tell, in the traditional and most common formulations, they are identical. <\/span><\/p>\n<\/blockquote>\n Here is the way I understand it. They are not identical. Excluded Middle is a law of logic, whereas Bivalence is a semantic principle. (See Michael Dummett, Truth and Other Enigmas<\/em>, Harvard UP, 2nd ed. , 1980, p. xix; Paul Horwich, Truth<\/em>, Oxford UP, 2nd ed., 1998, p. 79) If 'p' is a place-holder for a proposition, any proposition, then Excluded Middle is:<\/span><\/p>\n LEM. p v ~p.<\/span><\/p>\n<\/blockquote>\n If 'p' is a propositional variable, and we quantify over propositions, then we have the universal quantification<\/span><\/p>\n LEM*. For all p, p v ~p.<\/span><\/p>\n<\/blockquote>\n It is understood that the wedge in the above formulae signifies exclusive disjunction. Why is that understood? Because both p and not-p is excluded by the Law of Non-Contradiction:<\/span><\/p>\n LNC. ~(p & ~p). <\/span><\/p>\n<\/blockquote>\n If I may be permitted parenthetically to wax poetic in these aseptic precincts, (LNC) possesses a 'dignity' in excess of that possessed by (LEM). What I mean is that there are some fairly plausible counterexamples to (LEM), but none that are very plausible to (LNC). Few philosophers are dialetheists; many more accept truth-value gaps.<\/span><\/p>\n The laws of logic are purely formal: they abstract from content or meaning. They are syntactic principles. Bivalence, by contrast, is a semantic principle. It goes like this:<\/span><\/p>\n BV. Every proposition is either true or false.<\/span><\/p>\n<\/blockquote>\n Tertium non datur<\/em> means that a third is not given: there is no third truth value. (TND) is also a semantic principle:<\/span><\/p>\n TND. No proposition is neither true nor false.<\/span><\/p>\n<\/blockquote>\n So the difference between (LEM) and (BV) is that the first is a syntactic principle and the second a semantic principle. But is this a difference that makes a difference? Is there a conceivable case where (LEM) is true but (BV) false? I don't know the answers to these questions. Either that or I forgot them. But if you conflate the two principles, then you are in good company. W. V. O. Quine, Mathematical Logic<\/em>, Harvard UP, 8th ed., 1976, p. 51: ". . . the law of excluded middle,<\/em> which is commonly phrased as saying that every statement is either true or false . . . ."<\/span><\/p>\n","protected":false},"excerpt":{"rendered":" Dave Gudeman comments: I was surprised to see you distinguishing between bivalence and the LEM. As far as I can tell, in the traditional and most common formulations, they are identical. Here is the way I understand it. They are not identical. Excluded Middle is a law of logic, whereas Bivalence is a semantic principle. … Continue reading “Excluded Middle, Bivalence, and Tertium Non Datur<\/i>“<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[108],"tags":[],"class_list":["post-3983","post","type-post","status-publish","format-standard","hentry","category-logica-docens"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/3983","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/comments?post=3983"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/3983\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=3983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=3983"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=3983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
\n
\n
\n
\n
\n
<\/span><\/p>\n